Squares that can make an artist out of you

Ever since I first saw an Escher print with its cleverly interlocking figures, I have been fascinated by the subject of tessellations.

The word derives from the Latin "tessarae", meaning mosaic or tile, and is used in the mathematical sense to mean the art/science of covering areas completely with the same repeated shape, leaving no gaps between.

The word "art" is justified, as this geometrical method, in the hands of an Escher, becomes just that.

The disc-based program Tessellations, from Cambridge Micro Software, does not guarantee to turn you into an artist - but its design makes it extremely simple to get fantastic results.

By offering several small menus it uses the minimum of keys - the cursors for drawing, Spacebar and Return for menu selection, Shift and Delete for fixing a line or erasing it.

On start-up a square appears. Selecting "T", for tessellation, covers the screen with squares like a tiled floor.

Nothing in that, perhaps, but the first menu allows the user to rotate the square, or stretch it laterally or diagonally.

The resulting parallelograms can also be tessellated all over the screen, creating the basic underlying framework.

Following this the user can then change the outline shape, from plain straight lines, in two stages - "horizontals" and "verticals".

On the top line of the basic parallelogram appear two cur sors, a moveable square at one end and a cross fixed at the other.

The user directs the square around in stages, drawing its path by Shift presses. X-Y coordinates are given, and are needed, for really accurate geometrical work.

Any meandering line can be drawn in any of seven colours and the bottom line simultaneously repeats it.

The line must end at the cross, whereupon the same process is repeated at the sides. The shape can then be edited if necessary.

Additionally, a pattern can be created which lies within the boundary.

This can be based upon any one of nine variations on the three basic laws of symmetry - rotation, reflection or displacement.

When a particular pattern type is called, any line drawn within the parallelogram is acted upon under its rules - mirrored for example, or perhaps three fold (like a cloverleaf) -

Alternatively the outline can be left blank and only the "internal" pattern drawn. This would result in repeated shapes which do not join together in any way.

Calling tessellation put the drawing, to any desired scale, in the centre of the screen.

This area is then repeated pixel by pixel in all the corresponding areas dictated by the original parallelogram tessellation framework.

The speed of copying is dictated by the number of points laid out in the original and can be a bit slow, taking several minutes.

The basic underlying parallelogram pattern is not drawn but a clever bit of two-screen manipulation allows the user to call it up and see it superimposed.

I would thoroughly recommend this package, even though it is rather highly priced, to any school for work in areas of maths, art, home economics (for fabric designs) and any other application which requires the creation of superb repeating patterns.

Terry Hallard